Question

[Nguyễn Tiến Đạt]

Mina giúp mk vs!!!!!!!!!!

1)So sánh

a)\(\dfrac{12}{47}và\dfrac{11}{53}\) b)\(\dfrac{456}{461}và\dfrac{123}{128}\) c)\(\dfrac{12}{47}và\dfrac{19}{77}\)

d)\(A=\dfrac{13^{15}+1}{13^{16}+1}và\) \(B=\dfrac{13^{16}+1}{13^{17}+1}\)

P/s:Cherry Võ tag Trần Huyền Trang giùm cái please

Answer 1

[Thái Viết Nam]

a) \(\dfrac{12}{47}\) và \(\dfrac{11}{53}\)

Ta có: \(\dfrac{11}{47}>\dfrac{11}{53}\) mà \(\dfrac{12}{47}>\dfrac{11}{47}\)

\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)

Answer 2

[Tiểu Thư họ Nguyễn]

a) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{11}{44}>\dfrac{11}{53}\)

\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)

b) Ta có : \(\dfrac{456}{461}=1-\dfrac{5}{461}\)

\(\dfrac{123}{128}=1-\dfrac{5}{128}\)

Vì \(\dfrac{5}{461}< \dfrac{5}{128}\Rightarrow1-\dfrac{5}{461}>1-\dfrac{5}{128}\)

\(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\)

c) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{19}{76}>\dfrac{19}{77}\)

=> \(\dfrac{12}{47}>\dfrac{19}{77}\)

d) Ta có : \(13A=13.\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{16}+13}{13^{16}+1}=\dfrac{13^{16}+1+12}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)

\(13B=13.\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)

Ta thấy : \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\Rightarrow\dfrac{13^{15}+1}{13^{16}+1}>\dfrac{13^{16}+1}{13^{17}+1}\)